On lower transcendence degree
Recent developments in noncommutative algebraic geometry suggest that we need an invariant analogous to the transcendence degree of a field for division algebras not necessarily finite over their centers. Such an invariant is the Gelfand-Kirillov transcendence degree, denoted by Tdeg. The author defines for arbitrary associative algebras another such invariant, called the lower transcendence degree, denoted by Ld. The basic properties of Ld are established, and induction, faithful flatness and deformation theory are used to compute Ld. It is proved that \(\text{Ld}=\text{Tdeg}\) for various division algebras. Finally, Ld is used to study some open problems.
scientific article; zbMATH DE number 1236400
scientific article